Magnetic coupling in superconducting spin valves with strong ferromagnets

Magnetic coupling in superconducting spin valves with strong ferromagnets

Flokstra, M.G.; Knaap, J.M. van der; Aarts, J.

Citation

Flokstra, M. G., Knaap, J. M. van der, & Aarts, J. (2010). Magnetic coupling in

superconducting spin valves with strong ferromagnets. Physical Review B, 82, 184523.

doi:10.1103/PhysRevB.82.184523

Version: Not Applicable (or Unknown)

License: Leiden University Non-exclusive license Downloaded from: https://hdl.handle.net/1887/44543

Note: To cite this publication please use the final published version (if applicable).

Magnetic coupling in superconducting spin valves with strong ferromagnets

M. Flokstra, J. M. van der Knaap, and J. Aarts

Kamerlingh Onnes Laboratory, Leiden Institute of Physics, P.O. Box 9504, 2300 RA Leiden, The Netherlands 共Received 9 August 2010; published 15 November 2010兲

We investigate the magnetotransport behavior of ferromagnet共F兲/superconductor/ferromagnet trilayers made of ferromagnetic Ni₈₀Fe₂₀共Permalloy, Py兲 and superconducting Nb for temperatures both above and below the superconducting transition temperature T_c. In such devices, and for weak ferromagnets, T_c depends on the relative magnetization directions of the two F layers in such a way that T_c^Pof the parallel共P兲 alignment is lower than T_c^AP of the antiparallel 共AP兲 alignment 共the so-called superconducting spin-valve effect兲. For strong magnets, the suppression of Andreev reflection may alter this picture, but also stray field effects become important, as is known from earlier work. We compare large-area samples with microstructured ones, and find blocklike switching in the latter. We show this not to be due to a switch between the P and AP states, but rather to dipolar coupling between domains which are forming in the two Py layers, making a stray-field scenario likely. We also present measurements of the depairing共critical兲 current Idpand show that a similar depression of superconductivity exists far below T_cas is found around T_c.

DOI:10.1103/PhysRevB.82.184523 PACS number共s兲: 74.45.⫹c, 74.78.Fk, 75.60.Ch

I. INTRODUCTION

In multilayers of superconducting 共S兲 and ferromagnetic 共F兲 materials, one of the phenomena which has received much attention in the last few years is the so-called super- conducting spin-valve共SV兲 共or spin-switch兲 effect. First sug- gested by Buzdin et al.^1,2 and by Tagirov,³ the device con- sists of an F/S/F sandwich where a superconducting spacer, with a thickness d_Son the order of the superconducting co- herence length ␰S, separates two ferromagnetic layers with controllable magnetization directions. The calculations, per- formed in the weakly ferromagnetic limit 共meaning equal spin subbands兲 showed that for such a device the supercon- ducting transition temperature for parallel 共P兲 alignment of the magnetization in both F layers, T_c^P, is always lower than that for the antiparallel 共AP兲 alignment Tc

AP. Additionally, it should be possible to tune the device parameters共in particu- lar, the F layer thicknesses dF兲 such that superconductivity only appears in the AP alignment, leading to a controllable supercurrent through a small field manipulation. Experiments on macroscopic-sized spin-valve systems using weakly fer- romagnetic CuNi appeared to follow the theoretical prediction,^4,5although the difference in Tcbetween the P and the AP alignment was only a few millikelvin, much smaller than the calculations indicated, and reentrance was not found. Recent measurements on S/F bilayers made of Nb/

CuNi showed that a Tclowering of a few millikelvin is also found when the ferromagnet is in a domain state.⁶ This is basically due to the fact that Cooper pairs break less easily when they sample an inhomogeneous exchange field, which can be considered a lateral variant of the spin-valve effect.⁷ For spin-valve systems with strong ferromagnets, the situ- ation is more complicated. In a number of reports, with mag- nets such as Ni共Ref.8兲 or Ni80Fe₂₀共permalloy, Py兲,^9,10stan- dard spin-valve behavior T_c^AP⬎Tc

P was observed, with the difference between T_c^AP and T_c^P going up to 40 mK at low temperatures. In other experiments with Py,^11,12 Co, and Fe combined¹³or Co,¹⁴“inverse” behavior T_c^AP⬍Tc

Pwas found.

This was explained as either due to enhanced reflection of

spin-polarized quasiparticles共a mechanism not present in the calculations with equal spin subbands兲,¹¹or to the effects of stray fields from domain walls.^10,12–14 The difference be- tween the observations of the standard and the inverse effects appears to be that those experiments finding standard behav- ior make use of an antiferromagnetic pinning layer in order to have one layer with fixed, and one layer with a freely rotating magnetization, while the reports on the inverse ef- fect use a difference of dF or different materials for both layers in order to create a difference in coercive fields and thereby a field range where the magnetizations are AP. The pinning layer suppresses domain formation, and, in particu- lar, the work of Zhu et al. showed that if, in samples with a pinning layer, the free layer is brought in a domain state, the standard spin-valve effect is lost.¹⁰Focusing now on samples without pinning layer, almost all investigations were per- formed on共millimeter兲 large samples, where large amount of domains were present during the transition from the P to the AP state. In the work of Rusanov et al., samples were struc- tured down to micrometer size, and the switching of the magnetization was instantaneous, giving blocklike variations in the resistance, and suggesting that a clear P to AP switch was obtained.¹¹In such a case, it can still be argued that for strongly spin-polarized ferromagnets the P alignment may yield an enhanced Tc; in particular, in the limit of 100% spin polarization, the P alignment confines quasiparticles in the S layer because Andreev reflections are not possible while they still can leave the superconductor共one electron to each bank, in a crossed process兲 in the AP alignment.

In this work we examine the question whether also in micron-sized samples the inverse spin-valve effect is related to stray fields or due to the spin polarization. We present a series of measurements on Nb/Py bilayers and spin-valve devices, both with large sizes and microsized, where we compare anisotropic magnetoresistance 共AMR兲 effect in the normal state with the magnetoresistance measurements in the superconducting state. We find that, according to the AMR, domains also exist in micron-sized samples, and that the blocklike switching is presumably due to dipolar coupling between the domains in the two Py layers, acting as one.

1098-0121/2010/82共18兲/184523共7兲 184523-1 ©2010 The American Physical Society

This makes the stray field scenario likely. We also present measurements of the depairing共critical兲 current Idpfar below T_c and show that a similar depression of superconductivity exists in that temperature regime as found around Tc.

II. EXPERIMENTAL DETAILS

Nb/Py layers were grown on Si共100兲 substrates by dc magnetron sputtering in a ultrahigh-vacuum chamber with a background pressure of 10⁻⁹ mbar and an Ar pressure of 4 ␮bar for the Nb and 2.5 ␮bar for the Py, with Nb as bottom layer. The substrate holders were equipped with a small magnet to determine the direction of easy axis for the Py layers and enhance the fast switching properties. The Nb layer thickness was kept at 50 nm for all samples while for the Py layers thickness we used 20 and 50 nm. For our Py/

Nb/Py spin-valve devices the bottom Py layer is 50 nm thick and the top Py layer is 20 nm thick. All our devices have an additional 2 nm Nb capping layer added on top to prevent oxidation of the top Py layer. We show in the Appendix that not adding such protective layer leads to an exchange-biased Py layer, likely due to antiferromagnetic iron-oxide regions.

The Py has a degree of polarization close to 45% and a Curie temperature around 900 K. The thickness of the layers is far larger than the length ␰Fover which superconducting corre- lations are assumed to penetrate, which is around 1.5 nm.¹⁵ The purity of the Nb target is 99.95% which yields a Tcof 9.1–9.2 K for thick films. At the thickness of 50 nm, Tcof a single film is around 8.9 K, and from critical field measure- ments preformed earlier on similar samples we extract a zero-temperature Ginzburg-Landau 共GL兲 coherence length

␰GL共0兲⬇13 nm. This corresponds to a normal-state elastic mean-free path ᐉN⬇5.5 nm.¹¹

Standard electron-beam lithography was used to pattern both the microsized strips, with a length of 40 ␮^{m and a} width of 1 to 4 ␮m, and the large-scale devices 共2000

⫻200 ␮m²兲, where the direction of the strips are aligned with magnetic easy axis of the Py layer. These strips were etched down using Ar ion etching at a Ar pressure of 3 ␮^bar with a background pressure of 10⁻⁶ mbar. Au contacts were sputtered in a second deposition step using a lift-off resist mask technique. A few nanometer of Ti were sputter as ad- hesion layer for the Au. The contact geometry is four probe, with 10 ␮m spacing between the voltage probes. Figure 1

shows a scanning electron microscope 共SEM兲 image of a 40⫻2 ␮m²spin valve. This recipe is used for both bilayer and spin valve, both for microsized and macrosized devices although for the latter a spacing of 1000 ␮m between the voltage probes was used. Typical transition curves 共resis- tance R versus temperature T around Tc兲 for several of our devices are shown in Fig. 2, where for clarity curves are shifted along temperature. The typical width of the transition is 50–100 mK. Also shown in the figure are all Tc’s and low temperature resistances 共R0兲 for our devices. The choice for different layer thicknesses for the Py in the spin-valve device is to establish different coercive fields, making the device switchable from parallel to antiparallel. The coercive fields of the 20- and 50-nm-thick microsized Py strips are expected to be in the range from 0 to 20 mT 共Ref. 11兲 with a wider strip leading to a lower coercive field value共a large Py thin film of 20 nm thickness was measured to have a coercive field less than 0.5 mT兲. For our typical microsized strips 共1–4 ␮^{m wide}兲 we always found a difference of about 5 mT between the two different thicknesses. However, as we will show later, the mutual influence of the dipole fields prevents clean and uncorrelated switching. The microsized elongated structures were chosen to promote single domain switching.

They also have a sufficiently large cross-sectional resistance to perform critical current共Ic兲 measurements. We performed AMR measurements just above Tc to see if and when do- mains appear in our Nb/Py bilayer systems, and compared this to the AMR signal of the共spin-valve兲 trilayers. The re- sponse of the superconductor was found by comparing these AMR measurements to the magnetoresistance measurements in the transition. All measurements were done in a standard

4He cryostat with magnetic shielding to provide a low-noise environment. It is equipped with a superconducting coil to generate magnetic fields up to 1 T. All field measurements

40 x 2µm²trilayer strip (Py based no capping)

I⁺ V⁺ V⁻ I⁻

Si substrate Au leads

FIG. 1. SEM image of a four-probe 40⫻2 ␮m²spin-valve de- vice. The distance between the voltage probes 共V⁺ and V⁻兲 is 10 ␮m and the full length of the spin-valve wire is 40 ␮m. Similar Au contacting leads for the current probes are at the end points of the wire共not shown兲.

R/R0

T (K)

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.0

0.2 0.4 0.6 0.8 1.0

2000x200 BL20

40x4 BL50 40x1

SV

7.0 8.3

8.2 8.3

7.4 7.4 8.3

7.48 5.73

3.85 4.22

3.00 4.22 6.35 T_c(K) R₀(Ω) BL20

BL50 SV BL20 BL50 SV SV

40x42000x20040x1

FIG. 2. Temperature variation in the resistance around the tran- sition temperature T_cfor共from left to right兲 a Py共50兲/Nb共50兲/Py共20兲 spin valve 共SV兲, a Nb共50兲/Py共50兲 bilayer 共BL50兲 and a Nb共50兲/

Py共20兲 bilayer 共BL20兲, with numbers representing the layer thick- ness in nanometer. Resistance is normalized to the low-temperature resistance R₀and curves are shifted along temperature for clarity.

Lateral dimensions of the devices are given in the graph in units of

␮m². The table shows T_c and R₀ of all devices presented in this report.

FLOKSTRA, VAN DER KNAAP, AND AARTS PHYSICAL REVIEW B 82, 184523共2010兲

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were performed with the direction of the applied field along the long side of the strip, which implies field parallel to the measurement current. The critical current measurements were performed well below Tc, and probe the gap strength, enabling a comparison between P and AP below the transi- tion area. A pulsed current method was used for these mea- surements, which is described in Ref.16.

III. RESULTS A. R(H) for T⬎Tc

Figure3shows the result of R共H兲 measurements on large- scale Nb/Py bilayers and a Py/Nb/Py spin valve, all with lateral dimension 2000⫻200 ␮m²and at a temperature of 9 K 共Nb in normal state兲. All devices show the characteristic AMR dip, with a relative resistance change close to 0.06%.

The spin valve and bilayer with the thick Py layer 共50 nm兲 show a very similar hysteretic curve with a coercive field value close to 1 mT; the bilayer with the thin Py layer共20 nm兲 shows a much broader dip with a coercive field close to 3 mT. The same measurements but now on microstructured strips, all with lateral dimension 40⫻4 ␮^m2, are shown in Fig. 4. For the spin valve, block-shaped hysteretic dips ap- pear with switches near ⫾1 mT and ⫾3 mT, and with 共again兲 a relative resistance change of 0.06%. For both the 50-nm-thick and 20-nm-thick bilayer we do not see any AMR dip coming out of the measurement noise, pointing toward a single domain type of switching. The noise level is similar for all three devices and about 0.01%, which is 0.3– 0.4 m⍀ in terms of absolute resistance value. It is sig- nificantly worse compared to the large-scale devices and sug- gests that contacts to the strip are of less quality.

The appearance of this 共seemingly兲 two-step switch pro- cess in the microsized spin valve is very different from the large-scale spin valve. Yet, the size of the resistance change 共about 24 m⍀兲 is similar, and the observed switching fields

of the blocks coincide with the coercive fields of the two different large-scale bilayers. To further explore this block type of switching we fabricated a more narrow bridge共1 ␮^m wide兲 increasing the shape anisotropy energy, thus enhancing its importance in determining the possible domain states in the strips. Results are presented in Fig.5and show a series of R共H兲 measurements at constant temperature 共T=9 K兲 above

-20 -15 -10 -5 0 5 10 15 20

0.9976 0.9980 0.9984 0.9988 0.9992 0.9996 1.0000 BL20

R/R(µ0Ha=30mT)

µ0H_a(mT)

BL50

SV

T = 9 K

2000 x 200 µm²devices

FIG. 3. Resistance normalized to the value at 30 mT as function of the in-plane applied field H_aon large-scale devices with lateral dimension 2000⫻200 ␮m², all at temperature T = 9 K. From top to bottom, a Nb共50兲/Py共20兲 bilayer 共BL20兲, a Nb共50兲/Py共50兲 bilayer 共BL50兲, and a Py共50兲/Nb共50兲/Py共20兲 SV, with numbers representing the layer thickness in nm. The BL50 and SV curves are shifted by, respectively, −0.0008 and −0.0016.

-20 -15 -10 -5 0 5 10 15 20

0.9994 0.9996 0.9998 1.0000 1.0002

R/R(µ0Ha=30mT)

µ₀H_a(mT)

BL50 & BL20 (in noise)

SV

T = 9 K

40 x 4 µm²devices

FIG. 4. Resistance normalized to the value at 30 mT as a func- tion of the in-plane applied field H_a on microsized devices with lateral dimension 40⫻4 ␮m², all with temperature T = 9 K. The presented curve is from a Py共50兲/Nb共50兲/Py共20兲 spin valve while the results on the Nb共50兲/Py共20兲 and Nb共50兲/Py共50兲 bilayers 共BL20 and BL50兲 are “flat” and within the noise of the spin valve, with numbers representing the layer thickness in nanometer.

-15 -10 -5 0 5 10 15

0.960 0.965 0.970 0.975 0.980 0.985 0.990 0.995 1.000

R/R(µ0Ha=30mT)

µ0H_a(mT) 40 x 1 µm²spin-valve

T = 9 K

FIG. 5. Resistance normalized to the value at 30 mT as function of the in-plane applied field H_aon a 40⫻1 ␮m² Py共50兲/Nb共50兲/

Py共20兲 spin valve, with numbers representing the layer thickness in nanometer. All curves have a different magnetic history and are repeatedly shifted by −0.005. For all measurements the temperature was 9 K.

T_c, all with slightly different saturation histories. Although no two curves are identical, there seem to be only a limited number of values for the applied field where a jump in resis- tance is seen, and the size of those jumps take only few different values. The range over which hysteresis is found goes from ⫾共4–14兲 mT, which is significantly higher than in the other devices. Also the size of the resistance change is about ten times higher than in our wider devices, implying that more perpendicular domains共magnetization perpendicu- lar to the current direction兲 are sampled.

The 共almost兲 single block-type switching indicates that the F layers become magnetically coupled in the spin-valve device. This coupling appears to be such that a switching in the thinner layer共highest coercive field兲 is triggered by the switching of the thicker layer 共lowest coercive field兲. In the 40⫻4 ␮m²bilayer strips, the switching is not accompanied by domain formation but rather makes a fast single switch, most likely due to the enhanced shape anisotropy which fa- vors single domain switching. In a spin-valve device of the same lateral dimension the F layers become coupled, result- ing in a block-type switch process for the spin valve and the formation of domains. The measurements on the 40

⫻1 ␮^m2 spin valve show that a variety of possible domain states exists, which can be entered during the switching. In wider strips we have never observed such behavior.

B. R(H) for T⬍Tc

A similar set of measurements is performed inside the transition, with Nb superconducting. The R共H兲 are all taken at temperatures near the low end of the transition curve to improve temperature stability. The measured signal now comes predominantly from the superconductor which is shorting the ferromagnetic layers by percolation paths. Fur- thermore, AMR features are no longer visible due to the 共relative兲 high⳵^R/⳵T in the transition. Our typical 100 mK transition width, combined with a 10⁻⁴ relative resistance change corresponds to a temperature change of 0.01 mK, which is below our measurement control of about 0.3 mK.

Figure 6 shows the result of R共H兲 measurements on the large-scale devices 共2000⫻200 ␮^m2兲. While the bilayer with the 50-nm-thick Py layer does not show any hysteric feature, the bilayer with the 20-nm-thick Py layer shows clear hysteric peaks. Their location is around⫾8 mT, which is significantly higher than the corresponding AMR dips in the same device at ⫾3 mT. Also the spin valve shows such hysteretic peaks but located at lower fields around⫾1.5 mT, only slightly higher than the corresponding AMR dips in the same device. For the microsized devices 共40⫻4 ␮^m2兲 the same trend is observed共see Fig.7兲 with again no hysteretic feature in the bilayer with the 50-nm-thick Py layer while the bilayer with the 20-nm-thick Py layer and the spin valve both do show hysteretic peaks. In case of the bilayer, the peaks are located at ⫾4 mT 共a lower value compared to the large- scale devices兲. For the spin valve the peaks are now really block shaped, with switching fields at⫾1 mT and ⫾4 mT.

In Fig. 8we present the R共H兲 measurements on the smaller spin valve共40⫻1 ␮^m2兲, and make a direct comparison with the obtained T⬎Tcresults共of the same sample, see Fig.5兲.

Block-shaped peaks are observed 共where all measurements have different magnetization history兲 with switches at ⫾5 and ⫾10 mT. Furthermore, there is a striking resemblance between the observed blocks for T⬎Tc 共dips兲 and T⬍Tc

共peaks兲.

R(Ω)

µ0Ha(mT)

BL50

SV (+0.5)

BL20

2000 x 200 µm²devices

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

-20 -15 -10 -5 0 5 10 15 20

0.0 0.5 1.0 1.5 2.0

R(Ω)

FIG. 6. Resistance as a function of the in-plane applied field H_a on large-scale devices with lateral dimension 2000⫻200 ␮m², at temperatures on the low end of the transition curve 共Nb in super- conducting state兲. From top to bottom, a Nb共50兲/Py共20兲 bilayer 共BL20兲, a Nb共50兲/Py共50兲 bilayer 共BL50兲, and a Py共50兲/Nb共50兲/

Py共20兲 SV, with numbers representing the layer thickness in nm.

The BL50 curve is shifted by +0.5 and the BL20 curve is on the right-hand scale.

R(Ω)

µ₀H_a(mT)

SV

40 x 4 µm²devices

BL50 (+1.5) BL20

(-0.5)

-20 -15 -10 -5 0 5 10 15 20

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

0 1 2 3 4 5 6

BL50 R(Ω)

FIG. 7. Resistance as a function of the in-plane applied field H_a on microsized devices with lateral dimension 40⫻4 ␮m², at tem- peratures on the low end of the transition curve 共Nb in supercon- ducting state兲. From top to bottom, a Nb共50兲/Py共20兲 bilayer 共BL20兲, 2⫻ a Nb共50兲/Py共50兲 bilayer 共BL50兲, and 2⫻ a Py共50兲/Nb共50兲/

Py共20兲 SV, with numbers representing the layer thickness in nano- meter. Two curves are shifted共by −0.5 and +1.5兲 as indicated. The SV curves are on the right-hand scale.

FLOKSTRA, VAN DER KNAAP, AND AARTS PHYSICAL REVIEW B 82, 184523共2010兲

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C. I_c(H) for T well below T_c

The measurements so far all focus on temperatures closely around the transition 共T⬃Tc兲. To study the working of the spin valve well below Tc we conducted a series of critical current measurements as function of applied field, Ic共Ha兲 by measuring the current I-voltage V characteristic.

We used 3 ms current pulses, with an interval of several seconds and increasing in amplitude until the critical current is reached and the superconductor is driven in the normal state. The sample is initially cooled down in zero-field con- dition and the first measurement at a fixed temperature al- ways starts in zero applied field. The obtained I-V curves all showed a sharp jump from almost zero voltage to the normal state, which indicates that we are measuring a depairing cur- rent rather than the onset to vortex flow. This we 共consis- tently兲 found before on S films and S/F bilayers.^6,16,17 The measurement is thus directly sensitive to the amplitude of the superconducting gap, which limits the critical current. Addi- tionally, the value of Icis well defined due to the sharp tran- sition. The results for the 40⫻4 ␮^m2Nb/Py spin valve are shown in Fig. 9, where Ic共H兲 curves are presented at four temperatures well below T_c, which, in terms of the reduced temperature t = T/Tc go down to t = 0.5. All data show a blocklike dip for the increasing applied field 共coming from negative saturation兲 with switching fields around 0.5 and 3.5 mT, after which the curve becomes constant. The observed switching fields of the blocks do not show a temperature dependence but do show a diminishing effect for decreasing temperature. The uncertainty in the determination of Ic is about the step size for the increase in current 共1 ␮A兲. We interpret the lowering of I_cas a suppression of the supercon-

ducting gap. Because the gap increases in strength for lower temperature, it is not strange to see a diminishing effect of the percentage change. The switching fields coincide with the values found in the transport measurements close to T_c 共see Figs.4and7兲. Figure10shows the t = 0.94 curve for up to higher field values, and the standard decrease in Icdue to applied field becomes visible. Additionally, in the inset the actual I-V measurement at the highest used field共125 mT兲.

IV. DISCUSSION AND CONCLUSIONS

Summarizing the data, we can come to the following con- clusions. For temperatures above the transition 共Nb in nor-

R(Ω)

µ₀H_a(mT) 40 x 1 µm²spin-valve

(+2.5) (+5)

0.960 0.965 0.970 0.975 0.980

-15 -10 -5 0 5 10 15

0 2 4 6 8

R/R(µ0Ha=30mT)

FIG. 8. Comparison of the resistance as a function of the in- plane applied field H_aon a 40⫻1 ␮m²Py共50兲/Nb共50兲/Py共20兲 spin valve共numbers representing the layer thickness in nanometer兲 be- tween temperatures on the low end of the transition curve 共Nb in superconducting state兲 and above the transition temperature Tc共Nb in normal state兲. All curves have a different magnetic history. Left- hand scale: results for T⬍Tcwith curves repeatedly shifted by +2.5 as indicated. Right-hand scale: results for T⬎Tctaken from Fig.5.

Ic/Ic,max

µ₀H_a(mT) 40 x 4 µm²spin-valve

0 2 4 6 8 10

0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98

1.00 T/Tc= 0.50

T/T_c= 0.70

T/Tc= 0.90

T/Tc= 0.94

~9%

~5%

~2%

~1%

FIG. 9. Critical current measurements I_c, normalized to the maximum observed value I_c,maxfor each temperature, as function of the in-plane applied field H_a on a 40⫻4 ␮m² Py共50兲/Nb共50兲/

Py共20兲 spin valve. The curves represent different reduced tempera- tures T/Tc and are shifted for clarity by −0.03, −0.08 and −0.15.

The indicated percentages are the relative sizes of the dips. Arrows denote the direction of the field sweep.

Ic/Ic,max

µ₀H_a(mT)

0 25 50 75 100 125

0.90 0.92 0.94 0.96 0.98 1.00

0.2 0.4 0.6 0.8 1.0 1.2 0

1 2 3 4

V(mV)

I (mA) µ0Ha= 125 mT

FIG. 10. High-field behavior of the T/Tc= 0.94 critical current measurement as presented in Fig. 9. The inset shows the current voltage measurement of the curve for␮0H_a= 125 mT.

mal state兲 we find that the resistance changes are dominated by the AMR effect of the Py layers, with a relative resistance change of order 10⁻⁴. In large-scale devices, where domain formation is not limited by the size of the sample, the ob- served resistance dips in the bilayers with 20-nm- and 50- nm-thick Py appear at different fields. For the spin-valve structure we then expect to see all four resistance dips in the AMR. However, we observe a behavior very similar to the bilayer with 50-nm-thick Py, already giving an indication for coupling effects between the two F layers.

Going to the microscopic regime, we no longer observe any dips in the AMR signal of the bilayers, pointing to a fast single domain type of switching. However, in the spin valve we do observe AMR resistance changes. A two-stepped switching has appeared by going from large scale to micro- sized spin valves, most strongly pronounced in the thinnest 共1 ␮m wide兲 spin-valve structure. This is a strong indication that the single domain switching in the bilayers is replaced by domain formation, including magnetic coupling between the two Py layers.

For temperatures below the transition 共Nb superconduct- ing兲 we observe peaks in the resistance now originating from changes in the superconducting gap, with a relative resis- tance change of order 10⁻¹. Especially in the 1-␮m-wide spin valve, these peaks are mirror images of the dips in the corresponding AMR signals. This implies that the supercon- ductor does not influence/change the switching behavior of the spin valve; and that the suppression of the supercon- ductor is a direct effect of the presence of the stray fields from the coupled domains. Such coupling between the F lay- ers was found in experiments using antiferromagnetic pin- ning layers.

In the bilayers we only observe these peaks in the devices with 20-nm-thick Py but not in the devices with 50-nm-thick Py. This we attribute to different types of domain walls. It is known that for very thin Py layers the domain wall becomes of the Néel type while for thicker Py layers it is Bloch type.¹⁸ The crossover between the two is around a Py thickness of 35 nm, implying Néel walls in our 20-nm-thick Py bilayer and Bloch walls in our 50-nm-thick Py bilayers. Calculations on stray fields generated by domain walls shows a signifi- cantly higher magnitude for Néel walls than for Bloch walls,¹⁹which we believe is the source of the observed dif- ference in our bilayers.

A special remark concerns the point that no traces are found of an enhancement of the superconductivity by do- main averaging from Cooper pairs, as found before both in CuNi- and Py-based devices,^6,7 and also more recently in a different set of Py-based devices.²⁰ In particular, for the large-area bilayer sample BL20, enhanced superconductivity in the domain state might have been expected. This is most probably due to the fact that the switching behavior and do- main formation in Py are very sensitive to the relative orien- tations of easy axis and applied field 共see also Ref.21兲. Al- though the samples were grown in a small bias field, no further special alignment was performed in the present ex- periments, and stray fields now apparently win from domain averaging. Note, incidentally, that even stray fields can lead to Tc enhancement in F/S/F structures but that needs care- fully designed samples.²²

By going to lower temperatures and measuring the critical current, which is a direct measure for the superconducting gap strength, we observe that the suppression of supercon- ductivity is still present. The fields at which the suppression occurs overlaps with the peaks in the magnetotransport mea- surements and do not change with temperature. This indi- cates that also a well-developed gap is not changing the switching of the Py layers, and likely the spin valve is still dominated by the stray fields. In our I-V measurements we do not see traces of a vortex flow while the stray fields con- necting the two F layers should result in vortices. However, since the domain state seems to be unaffected by the gap, we believe it strong enough to keep any vortices in place. Effec- tively, all vortices generated by the stray fields are strongly pinned by the共rigid兲 domain state itself.

ACKNOWLEDGMENTS

We acknowledge C. Bell and M. Hesselbert for discus- sions and technical support. This work is part of the research program of the Foundation for Fundamental Research on Matter共FOM兲, which is part of the Netherlands Organization for Scientific Research共NWO兲.

APPENDIX: EXCHANGE BIASED Py

All presented data so far were on devices where the top Py layer is covered by a thin Nb layer to protect it from oxidizing. Magnetoresistance measurements on a 40

⫻2 ␮m² bilayer strip without such capping layer is pre- sented in Fig. 11, where R共H兲 at room temperature 共T

= 300 K兲 is compared with low temperature 共T=10 K兲. At room temperature the AMR signal contains the typical dips.

They are symmetrical around zero field, with a coercive field of⫾6 mT, and with a relative resistance change of 0.05. At

R/R(µ0Ha=30mT)

µ₀H_a(mT)

R₁₀= 28 Ω R₃₀₀= 53 Ω (+0.006)

T = 10 K

40 x 4 µm²bilayer (unprotected)

-20 -15 -10 -5 0 5 10 15 20

0.982 0.988 0.994 1.000

1.006 T = 300 K

FIG. 11. Resistance normalized to the value at 30 mT as a func- tion of the in-plane applied field H_a on a 40⫻4 ␮m² Nb/Py bi- layer, for T = 300 K and T = 10 K. The respective resistances are indicated by R₃₀₀and R₁₀. Both the Nb layer and Py layer are 20 nm thick.

FLOKSTRA, VAN DER KNAAP, AND AARTS PHYSICAL REVIEW B 82, 184523共2010兲

184523-6

low temperature the dips have become broader, the coercive fields have become larger but the curve is no longer symmet- ric around zero field. The coercive fields are now at −14 and 9 mT, which indicates an exchange bias of 2.5 mT共such that

unbiased the coercive fields would be symmetric again at

⫾11.5 mT兲. We expect this exchange bias to be the result of the formation of Fe₂O₃ at the top of the Py layer, which becomes antiferromagnetic below 250 K.

1A. I. Buzdin, A. V. Vedyayev, and N. V. Ryzhanova,Europhys.

Lett. 48, 686共1999兲.

2A. I. Buzdin,Rev. Mod. Phys. 77, 935共2005兲.

3L. R. Tagirov,Phys. Rev. Lett. 83, 2058共1999兲.

4J. Y. Gu, C.-Y. You, J. S. Jiang, J. Pearson, Y. B. Bazaliy, and S.

D. Bader,Phys. Rev. Lett. 89, 267001共2002兲.

5A. Potenza and C. H. Marrows, Phys. Rev. B 71, 180503共R兲 共2005兲.

6M. Flokstra and J. Aarts,Phys. Rev. B 80, 144513共2009兲.

7A. Y. Rusanov, M. Hesselberth, J. Aarts, and A. I. Buzdin,Phys.

Rev. Lett. 93, 057002共2004兲.

8I. C. Moraru, W. P. Pratt, Jr., and N. O. Birge,Phys. Rev. Lett.

96, 037004共2006兲.

9I. C. Moraru, W. P. Pratt, and N. O. Birge, Phys. Rev. B 74, 220507共R兲 共2006兲.

10J. Zhu, X. Cheng, C. Boone, and I. N. Krivorotov,Phys. Rev.

Lett. 103, 027004共2009兲.

11A. Y. Rusanov, S. Habraken, and J. Aarts, Phys. Rev. B 73, 060505共R兲 共2006兲.

12D. Stamopoulos, E. Manios, and M. Pissas, Phys. Rev. B 75,

184504共2007兲.

13R. Steiner and P. Ziemann,Phys. Rev. B 74, 094504共2006兲.

14G. Carapella, F. Russo, and G. Costabile, Phys. Rev. B 78, 104529共2008兲.

15J. W. A. Robinson, S. Piano, G. Burnell, C. Bell, and M. G.

Blamire,Phys. Rev. Lett. 97, 177003共2006兲.

16A. Y. Rusanov, M. B. S. Hesselberth, and J. Aarts,Phys. Rev. B 70, 024510共2004兲.

17C. Cirillo, A. Rusanov, C. Bell, and J. Aarts,Phys. Rev. B 75, 174510共2007兲.

18T. Trunk, M. Redjdal, A. K’akay, M. F. Ruane, and F. B. Hum- phrey,J. Appl. Phys. 89, 7606共2001兲.

19M. Redjdal, J. H. Giusti, M. F. Ruane, and F. B. Humphrey, IEEE Trans. Magn. 39, 2684共2003兲.

20A. Y. Rusanov, T. E. Golikova, and S. V. Egorov, JETP Lett. 87, 175共2008兲.

21T.-J. Hwang and D. H. Kim, J. Korean Phys. Soc. 48, 1133 共2006兲.

22W. Gillijns, A. Y. Aladyshkin, M. Lange, M. J. Van Bael, and V.

V. Moshchalkov,Phys. Rev. Lett. 95, 227003共2005兲.